Step 1: Understanding the Question:
We are tasked with identifying the single alkyl halide compound from the options that is optically inactive due to the absence of an asymmetric chiral carbon center.
Step 2: Detailed Explanation:
A compound is classified as optically active if it contains a chiral carbon atom bonded to four entirely distinct groups. Let's analyze the structures of the options:
3-Chlorohexane: The $\text{C}_3$ position connects to -H, -Cl, an ethyl group, and a propyl group. It is chiral.
2-Chloro-3-methylbutane: The $\text{C}_2$ position connects to -H, -Cl, a methyl group, and an isopropyl group. It is chiral.
2-Chloropentane: The $\text{C}_2$ position connects to -H, -Cl, a methyl group, and a propyl group. It is chiral.
2-Chloro-2-methylbutane: Let us write out its detailed structural configuration around the $\text{C}_2$ central carbon:
$$ \text{CH}_3-\text{C(Cl)(CH}_3)-\text{CH}_2-\text{CH}_3 $$
Inspecting this central carbon ($\text{C}_2$) reveals it is bound to:
1. A chlorine atom (-Cl)
2. An ethyl group ($\text{-CH}_2\text{CH}_3$)
3.
Two identical methyl groups ($\text{-CH}_3$)
Because it contains two identical methyl groups, the central carbon is achiral. This symmetry renders the entire molecule optically inactive.
Step 3: Final Answer:
The optically inactive structure is 2-Chloro-2-methylbutane, matching option (A).